What I will do is use an Alpha-Beta algorithm with Quiescent search.
Sounds nice right? :)
Alpha-Beta is the basic search, I will go through that in my next post.
Quiescent is a kind of extension to the basic search which looks at captures only. More about this later.
Since Alpha-Beta search relies heavily on move ordering (as we will see), I will have to implement a good sorting algorithm as well.
Also we need to be able to evaluate positions. To start with I will only use piece values to put scores on positions. Once we get the search up and running efficiently we can improve and tweak the evaluation as much as we want, this is the fun part. :)
All this together will make for a good solid engine. We can extend it with all kinds of things further on.